1. Field of the Invention
The present invention relates to an image reconstructing apparatus and an image reconstructing method.
2. Description of the Related Art
Conventionally, a Filtered Back Projection (FBP) method is performed as a method of reconstructing a tomographic image from projection data based upon X-rays or gamma rays using a radiodiagnosis apparatus such as an X-ray Computed Tomography (CT) apparatus, a Positron Emission computed Tomography (PET) apparatus, a Single Photon Emission Computed Tomography (SPECT), or non-destructive examination equipment.
The FBP method is an image reconstructing method that uses the Central Section Theorem which states that “a Fourier transform of a projection toward a direction of an original image is equal to a section that is perpendicular to the projection direction and runs through the center in a two-dimensional Fourier transform of the original image.” The Central Section Theorem is explained below with reference to FIG. 11. FIG. 11 is a schematic diagram for explaining the Central Section Theorem.
First of all, as shown in FIG. 11, it is assumed where (x, y) denotes a rotating coordinate system having an inclination of an angle “ϕ” to an orthogonal coordinate system at rest (X, Y) in a real-space having the origin at a scan center, and “F” denotes data two-dimensionally Fourier-transformed from an original image “f”.
As shown in FIG. 11, The Central Section Theorem is that data that is one-dimensionally Fourier-transformed from projection data in a projection direction parallel to the “y axis” of the original image “f” is equal to the cross section of “F” with the perpendicular plane of the “k axis” having the inclination of the angle “ϕ” to an orthogonal coordinate system at rest (VX, VY) in a frequency space.
In other words, according to the Central Section Theorem, by one-dimensionally Fourier-transforming each of projection data in each projection direction, data “F” that is two-dimensionally Fourier-transformed from the original image “f” can be obtained.
According to the FBP method, sinogram data that the projection data in each projection direction is summed with respect to each coordinate section is Fourier-transformed, and then, for example, low-pass filter processing such as Ramp filtering for deleting high-frequency component is performed to remove statistical noise. According to the FBP method, a tomographic image is reconstructed by sequentially performing an inverse Fourier transform and back projection processing on the filtered Fourier-transformed data (for example, see “Medical Image/Radiological Equipment Hand Book” edited by Japan Industries Association of Radiological Systems, published by Nago Bijutsu Insatsu Kabushiki Kaisha, 2001, pp. 143-146).
According to the conventional technology described above, a high-frequency component that is deleted through the low-pass filter includes information for reproducing a profile of a structure through which radioactive rays have passed.
For this reason, the conventional technology as described above has a problem that because statistical noises are removed, the profile of the structure on a reconstructed image is blurred in an adverse manner that the picture quality of the reconstructed image is degraded.